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The Physics and Mathematics of THE SECOND LAW OF THERMODYNAMICS
, 1999
"... The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy constructed here is defined only for equilibrium states and n ..."
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Cited by 32 (3 self)
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The essential postulates of classical thermodynamics are formulated, from which the second law is deduced as the principle of increase of entropy in irreversible adiabatic processes that take one equilibrium state to another. The entropy constructed here is defined only for equilibrium states and no attempt is made to define it otherwise. Statistical mechanics does not enter these considerations. One of the main concepts that makes everything work is the comparison principle (which, in essence, states that given any two states of the same chemical composition at least one is adiabatically accessible from the other) and we show that it can be derived from some assumptions about the pressure and thermal equilibrium. Temperature is derived from entropy, but at the start not even the concept of ‘hotness’ is assumed. Our formulation offers a certain clarity and rigor that goes beyond most textbook discussions of the second law.
Computer Learning and the Scientific Method: A Proposed Solution to the Information Theoretical Problem of Meaning
, 1965
"... This discussion outlines and implements the theory of an inductive inference technique that automatically discovers classes among large numbers of input patterns, generates operational definitions of class membership with explicit levels of confidence, creates a continuously updated "selforganized" ..."
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Cited by 9 (3 self)
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This discussion outlines and implements the theory of an inductive inference technique that automatically discovers classes among large numbers of input patterns, generates operational definitions of class membership with explicit levels of confidence, creates a continuously updated "selforganized" coded hierarchical taxonomic classification of patterns, and recognizes to which already discovered class or classes, if any, a new input belongs in an informationtheoretically efficient way. Relationships to the "scientific method" and learning are discussed.
Orthogonal Functions on the Unit Disk having Invariance in Form
, 1996
"... Consider the vector space of complex valued functions on the unit disk, and the Euclidean inner product. The Zernike, pseudoZernike and Orthogonal FourierMellon functions each define an orthogonal basis on this inner product space. This paper traces through the derivation of each set of functions. ..."
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Cited by 8 (8 self)
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Consider the vector space of complex valued functions on the unit disk, and the Euclidean inner product. The Zernike, pseudoZernike and Orthogonal FourierMellon functions each define an orthogonal basis on this inner product space. This paper traces through the derivation of each set of functions. 1 Introduction Consider the vector space of complex valued functions on the unit disk D 2 = \Phi (x; y) 2 R 2 : x 2 + y 2 1 \Psi If we take the Euclidean inner product hf; gi = ZZ D 2 f(x; y)g (x; y) dx dy we have the idea of orthogonality. The Zernike, pseudoZernike and Orthogonal FourierMellon functions each define an orthogonal basis for the corresponding inner product space. This paper traces through the derivation of each set of functions. The material presented draws heavily from [3] and [10], other important sources being [2], Appendix VII from [5] 1 and [9]. 1 Essentially duplicates [3]. 2 Invariance in Form Our basis functions are constructed such tha...
Ten theses on black hole entropy
"... I present a viewpoint on black hole thermodynamics according to which the entropy: derives from horizon “degrees of freedom”; is finite because the deep structure of spacetime is discrete; is “objective ” thanks to the distinguished coarse graining provided by the horizon; and obeys the second law o ..."
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Cited by 5 (0 self)
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I present a viewpoint on black hole thermodynamics according to which the entropy: derives from horizon “degrees of freedom”; is finite because the deep structure of spacetime is discrete; is “objective ” thanks to the distinguished coarse graining provided by the horizon; and obeys the second law of thermodynamics precisely because the effective dynamics of the exterior region is not unitary. Probably few people doubt that the twin phenomena of black hole entropy and evaporation hold important clues to the nature of quantum spacetime, but the agreement pretty much ends there. Starting from the same evidence, different workers have drawn very different, and partly contradictory, lessons. On one hand, there is perhaps broad agreement that the finiteness of the entropy points to an element of discreteness in the deep structure of spacetime. On the other hand there is sharp disagreement over whether the thermal nature of the Hawking radiation betokens an essential failure of unitarity in quantum gravity or whether it is instead betraying the need for a radical revision of the spacetime framework, as contemplated for instance in the “holographic principle”. These alternatives are not necessarily in contradiction, of course, but in practice, the wish to retain unitarity has been one of the strongest motivations for taking seriously the latter type of possibility. My own belief is that nonunitarity is probably inevitable in connection with gravity and that,
Quantum Philosophy: The Flight from Reason
 in Science
"... I want to discuss a rather delicate matter concerning a notoriously difficult subject, the foundations of quantum mechanics, a subject that has inspired a great many peculiar proclamations. Some examples: and... the idea of an objective real world whose smallest parts exist objectively in the same s ..."
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Cited by 4 (0 self)
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I want to discuss a rather delicate matter concerning a notoriously difficult subject, the foundations of quantum mechanics, a subject that has inspired a great many peculiar proclamations. Some examples: and... the idea of an objective real world whose smallest parts exist objectively in the same sense as stones or trees exist, independently of whether or not we observe them... is impossible... [1] We can no longer speak of the behavior of the particle independently of the process of observation. As a final consequence, the natural laws formulated mathematically in quantum theory no longer deal with the elementary particles themselves but with our knowledge of them. Nor is it any longer possible to ask whether or not these particles exist in space and time objectively...... Science no longer confronts nature as an objective observer, but sees itself as an actor in this interplay between man and nature. The scientific method of analysing, explaining, and classifying has become conscious of its limitations... method and object can no longer be separated. [2] and
Hidden Variables and Nonlocality in Quantum Mechanics
, 1996
"... At the present time, most physicists continue to hold a skeptical attitude toward the proposition of a ‘hidden variables ’ interpretation of quantum theory, in spite of David Bohm’s successful construction of such a theory and John S. Bell’s strong arguments in favor of the idea. Many are convinced ..."
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At the present time, most physicists continue to hold a skeptical attitude toward the proposition of a ‘hidden variables ’ interpretation of quantum theory, in spite of David Bohm’s successful construction of such a theory and John S. Bell’s strong arguments in favor of the idea. Many are convinced either that it is impossible to interpret quantum theory in this way, or that such an interpretation would actually be irrelevant. There are essentially two reasons behind such doubts. The first concerns certain mathematical theorems (von Neumann’s, Gleason’s, Kochen and Specker’s, and Bell’s) which can be applied to the hidden variables issue. These theorems are often credited with proving that hidden variables are indeed ‘impossible’, in the sense that they cannot replicate the predictions of quantum mechanics. Many who do not draw such a strong conclusion nevertheless accept that hidden variables have been shown to exhibit prohibitively complicated features. The second reason hidden variables are disregarded is that the most sophisticated example of a hidden variables theory—that of David Bohm—exhibits nonlocality, i.e., it can happen in this
Towards a Motivational Theory of Technology IMPLEMENTATION PROCESSES
, 2007
"... Managing the selection and implementation of information technology is a critically important activity, but significant gaps exist in our understanding of that process. This paper proposes an alternative research approach, in which the motivation to implement a system is the starting point for under ..."
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Cited by 1 (0 self)
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Managing the selection and implementation of information technology is a critically important activity, but significant gaps exist in our understanding of that process. This paper proposes an alternative research approach, in which the motivation to implement a system is the starting point for understanding subsequent adoption processes. The paper has three main components: first we justify the use of motivation as the key to understanding adoption activities and outcomes for bundled (divisible) technologies. We then illustrate the operation of our theory with simplified examples of interorganizational system implementations. Finally, we list key conceptual and methodological requirements for analyzing implementation processes using this method.
Locality, Weak or Strong Anticipation and Quantum Computing. I. Nonlocality in Quantum Theory
"... Abstract The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the ChurchTuring hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Categ ..."
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Abstract The universal Turing machine is an anticipatory theory of computability by any digital or quantum machine. However the ChurchTuring hypothesis only gives weak anticipation. The construction of the quantum computer (unlike classical computing) requires theory with strong anticipation. Category theory provides the necessary coordinatefree mathematical language which is both constructive and nonlocal to subsume the various interpretations of quantum theory in one pullback/pushout Dolittle diagram. This diagram can be used to test and classify physical devices and proposed algorithms for weak or strong anticipation. Quantum Information Science is more than a merger of ChurchTuring and quantum theories. It has constructively to bridge the nonlocal chasm between the weak anticipation of mathematics and the strong anticipation of physics.
1 The First Law of Thermodynamics 1.1 ELEMENTS OF THERMODYNAMICS TERMINOLOGY
"... The first step in the thermodynamic analysis of anything must be the definition of the entity that is being subjected to analysis. We refer to this entity (collection of matter, region in space) as a system. Although the need for executing this first move and for doing it once and unambiguously is o ..."
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The first step in the thermodynamic analysis of anything must be the definition of the entity that is being subjected to analysis. We refer to this entity (collection of matter, region in space) as a system. Although the need for executing this first move and for doing it once and unambiguously is obvious, the temptation is great to assume the system definition itself obvious and omit it. This is a source of confusion, if not outright error. Paradoxical differences between two results claimed by two experts who attack ‘‘the same problem’’ are often explained by the realization that the two problem solvers were mentally addressing different systems. As we will see very soon, the precise definition of the system is critical when determining the location and magnitude of thermodynamic irreversibility. The tendency to forget to define the system is due mainly to tradition. In considerably older disciplines such as solidbody mechanics, the system is indeed obvious, as the mere sketching of a body focuses the attention of both problem solver and critic. In fluid mechanics and heat transfer, the system is
Dependent Coorigination and Inherent Existence: DualAspect Framework
"... Copyright © 2009 (except quotes used from other authors) by Ram Lakhan Pandey Vimal and ..."
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Copyright © 2009 (except quotes used from other authors) by Ram Lakhan Pandey Vimal and